Herman Rubin wrote: > On 2013-06-03, Peter Percival <email@example.com> wrote: >> Herman Rubin wrote: > > >>> Mathematical logic is not all of logic, but it is logic, not >>> mathematics. There is more to the logic which is used by >>> mathematicians, such as in metamathematics, than is in the >>> first order predicate calculus, which is what is used in >>> mathematical proofs. There are metamathematical proofs of >>> mathematical theorems which do not have mathematical proofs. > >>> There is also inductive logic, which is best represented by >>> statistical decision theory, and there are modal logics. I >>> have seen description of "quantum logics", but I do not see >>> them as more than partial representations. > >> What is mathematical logic? Is it logic studied with mathematical > > It is the first order predicate calculus based on Boolean > sentential calculus. That is, predicates cannot be > quantified, only individuals can. Nor can predicates > be arguments of other predicates.
Why? Do mathematicains neither use nor study higher order logic? I seem to recall that various useful concepts are not expressible in first order predicate calculus. Also, are not intuitionists mathematicisn? No Boolean sentential calculus for them. Is not the lack of categoricity a limitation? Do not mathematicians when reasoning informally use types? Why should that informal reasoning be formalised and studied?
-- I think I am an Elephant, Behind another Elephant Behind /another/ Elephant who isn't really there.... A.A. Milne